Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
416 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22626204 | C2 | semidirect |
| 2. #22625064 | C2 | semidirect |
| 3. #22625062 | C2 | semidirect |
| 11. #17988966 | C4 | semidirect |
| 14. #17988959 | C4 | semidirect |
| 15. C2×C4×#10596831 | C4 | semidirect |
| 16. #532×C73 | C4 | semidirect |
| 129. C73 | #13583 | semidirect |
| 132. #532 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626204 | 2 |
| #22625064 | 2 |
| #22625062 | 2 |
| #22620357 | 2 |
| #13583 | 73 |